Avalanche phenomena use steeply nonlinear dynamics to generate disproportionately large responses from small perturbations, and are found in a multitude of events and materials1. Photon avalanching enables technologies such as optical phase-conjugate imaging2, infrared quantum counting3 and efficient upconverted lasing4-6. However, the photon-avalanching mechanism underlying these optical applications has been observed only in bulk materials and aggregates6,7, limiting its utility and impact. Here we report the realization of photon avalanching at room temperature in single nanostructures-small, Tm3+-doped upconverting nanocrystals-and demonstrate their use in super-resolution imaging in near-infrared spectral windows of maximal biological transparency. Avalanching nanoparticles (ANPs) can be pumped by continuous-wave lasers, and exhibit all of the defining features of photon avalanching, including clear excitation-power thresholds, exceptionally long rise time at threshold, and a dominant excited-state absorption that is more than 10,000 times larger than ground-state absorption. Beyond the avalanching threshold, ANP emission scales nonlinearly with the 26th power of the pump intensity, owing to induced positive optical feedback in each nanocrystal. This enables the experimental realization of photon-avalanche single-beam super-resolution imaging7 with sub-70-nanometre spatial resolution, achieved by using only simple scanning confocal microscopy and without any computational analysis. Pairing their steep nonlinearity with existing super-resolution techniques and computational methods8-10, ANPs enable imaging with higher resolution and at excitation intensities about 100 times lower than other probes. The low photon-avalanching threshold and excellent photostability of ANPs also suggest their utility in a diverse array of applications, including sub-wavelength imaging7,11,12 and optical and environmental sensing13-15.